Find the limit (if it exists). $$\lim _ { \Delta x \rightarrow 0 } \frac { ( x + \Delta x ) ^ { 2 } - 9 ( x + \Delta x ) + 2 - \left( x ^ { 2 } - 9 x + 2 \right) } { \Delta x }$$
A) $\frac { 1 } { 3 } x ^ { 3 } - \frac { 9 } { 2 } x ^ { 2 } + 2 x$
B) $2 x - 9$
C) $x ^ { 3 } - 9 x ^ { 2 } + 2 x$
D) $x ^ { 2 } - 9 x + 2$
E) does not exist

Question

Quizplus · Accepted Answer

This limit represents the derivative of the function $f(x) = x^2 - 9x + 2$ with respect to $x$. Simplifying the expression inside the limit gives $2x - 9$, which is the derivative of $f(x)$.

Find the Limit (If It Exists) lim⁡Δx→0(x+Δx)2−9(x+Δx)+2−(x2−9x+2)Δx\lim _ { \Delta x \rightarrow 0 } \frac { ( x + \Delta x ) ^ { 2 } - 9 ( x + \Delta x ) + 2 - \left( x ^ { 2 } - 9 x + 2 \right) } { \Delta x }Δx→0lim​Δx(x+Δx)2−9(x+Δx)+2−(x2−9x+2)​

Find the Limit (If It Exists) $\lim _ { \Delta x \rightarrow 0 } \frac { ( x + \Delta x ) ^ { 2 } - 9 ( x + \Delta x ) + 2 - \left( x ^ { 2 } - 9 x + 2 \right) } { \Delta x }$